Three identical spheres each of mass M are placed at the corners of a right angled triangle with mutually perpendicular sides equal to 3 m each…

Question

Three identical spheres each of mass M are placed at the corners of a right angled triangle with mutually perpendicular sides equal to 3 m each. Taking point of intersection of mutually perpendicular sides as origin, the magnitude of position vector of centre of mass of the system will be √x m. The value of x is

MARKS Content Team · Accepted Answer

Correct answer: 2. The diagram represents the locations of the masses as mentioned in the question. For point 1, r_1→=0i^+0j^ for point 2, r_2→=3i^+0j^ and for point 3, r_3→=0i^+3j^. The formula for centre of mass is r→_com=(m_1r_1→+m_2r_2→+m_3r_3→)/(m_1+m_2+m_3) ⇒r→_com=(M0i^+0j^+M3i^+M3j^)/3M ⇒r→_com=i^+j^ r→_com=√(1^2+1^2)=√2=√x ⇒x=2

Solution

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